1-8x^2=-767

Solution for 1-8x^2=-767 equation:

1-8x^2=-767

We move all terms to the left:

1-8x^2-(-767)=0

We add all the numbers together, and all the variables

-8x^2+768=0

a = -8; b = 0; c = +768;
Δ = b2-4ac
Δ = 02-4·(-8)·768
Δ = 24576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24576}=\sqrt{4096*6}=\sqrt{4096}*\sqrt{6}=64\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{6}}{2*-8}=\frac{0-64\sqrt{6}}{-16}
=-\frac{64\sqrt{6}}{-16}
=-\frac{4\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{6}}{2*-8}=\frac{0+64\sqrt{6}}{-16}
=\frac{64\sqrt{6}}{-16}
=\frac{4\sqrt{6}}{-1}
$